1. At a minimum you need to know if your profit expectancy (as a function of win rate and size of wins and losses) is positive, that does not necessarily involve any math but you need to know the equation and understand its implications. It's very simple but some people posting over the years can't grasp it, as exemplified when they're raving about their 96% win rate until suddenly they go quiet. Oh yeah, and that financial returns are not normally distributed.
How else are you going to define it? You study the market and find something that you can exploit for a probable profit. If you can find a coin flip that comes up heads 55% of the time you have an edge. If you could find a black jack game where you got to see both of the dealers cards you have an edge. If you bet on the direction a stock will go, cut your losses quickly and let your winners run, you have an edge.
It is nothing more than constructing a trading system, backtesting it over a large enough sample then, using the expectation formula to determine if you have a trading edge. That is, you need to have a positive expectation like the Las Vegas casinos. Any game you play in the casinos has an edge for the casinos at the expense of the gamblers. Gamblers are playing those games under negative expectation. To make monies in the stockmarket, you have to have an edge or positive expectation. If not, you are merely gambling. This article on expected value is from Investopedia.com https://www.investopedia.com/terms/e/expected-value.asp
Isn't this what quants do, day in and day out? They use statistical model for their algos, which is pretty much all math-driven.